whisk together the sake, mirin, soy sauce, and ginger in a small bowl.
Set aside.
Season the salmon on both sides with salt and pepper.
Heat a medium nonstick skillet over medium-high heat. Add the vegetable oil and swirl to coat the pan. When shimmery wavy lines run through the oil, place the salmon in the pan, skin-side down, and sear for 6 minutes. Tilt the pan occasionally to redistribute the oil as the salmon cooks.
Gently flip the salmon over and cook the other side for 2 minutes. Add more oil, 1 teaspoon at a time, if needed.
Transfer the salmon to a clean plate and, using a paper towel, wipe the oil from the skillet. Pour the prepared sauce into the skillet and bring to a boil over medium-high heat. Cook until the sauce has reduced by one-third, about 3 minutes.
Return the salmon to the pan, skin-side up, and spoon the reduced sauce over the top. Keep cooking for another 2 minutes, until an instant-read thermometer inserted into the thickest part of the fish reads 125°F.
The flesh should change to opaque pink and, when flaked with a fork, reveal a softer, slightly translucent pink toward the centre.
Divide the rice between four plates. Place the salmon on top of each. Spoon the excess sauce from the pan over the salmon and rice.
Garnish with the sesame seeds and scallions and serve.